document.write( "Question 1147780: “A quartic function in the form f(x) = ax^4 + bx^3 + cx^2 + dx + e is such that the coefficient of the quadratic and linear terms are 10 and -18 respectively. Additionally, f(0) =9 and x=1 is a root with a multiplicity of two. What is the value of (a +b)? \n" ); document.write( "

Algebra.Com's Answer #769153 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "It is clear from the condition that c= 10, d= -18  and  e= f(0) = 9.\r\n" );
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document.write( "So, the polynomial is  f(x) = ax^4 + bx^3 + 10x^2 - 18x + 9.\r\n" );
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document.write( "Now, substitute x= 1 into the last expression for the polynomial and take into account that x= 1 is the root.\r\n" );
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document.write( "You will get\r\n" );
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document.write( "    f(1) = a + b + 10 - 18 + 9 = 0,\r\n" );
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document.write( "which implies\r\n" );
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document.write( "    a + b = -10 + 18 - 9 = -1.    ANSWER\r\n" );
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